SUMMARY Unemployment is continuously increasing worldwide because of enormous increase in population. This paper attempts to propose an optimal control policy for a deterministic unemployment model. The model considers three states, namely, unemployment, employment, and newly created vacancies. Factors like retirement and death of employed persons, termination from job, and so forth are also included in the model. The optimal control analysis for proposed unemployment model is performed using Pontryagin's maximum principle. The conditions for optimal control of the unemployment problem with effective use of implemented policies to provide employment to unemployed persons and to create new vacancies are derived and analyzed. Copyright © 2015 John Wiley & Sons, Ltd.

Key words and Phrases: estimation of reliability; uniformly minimum variance unbiased estimator; maximum likelihood estimator; stressstrength model; Cramer-Rao lower bound; parallel system.ABSTRACT Uniformly minimum variance unbiased estimator ( W E ) of reliability in stress-strength model (known stress) is obtained for a multicomponent survival model based on exponential distributions for parallel system. The variance of this estimator is compared with Cramer-Rao lower bound (CRB) for the variance of unbiased estimator of reliability, and the mean square error (MSE) of maximum likelihood estimator of reliability in case of two component system.

The study endeavors to provide statistical inference for a (1 + 1) cascade system for exponential distribution under joint effect of stress-strength attenuation factors. Estimators of reliability function are obtained using Maximum Likelihood Estimator (MLE) and Uniformly Minimum Variance Unbiased Estimator (UMVUE) of the parameters. Asymptotic distribution of the parameters is also obtained. Comparison between estimators is made using data obtained through simulation experiment.

The reliability function for a parallel system of two identical components is derived from a stress-strength model, where failure of one component increases the stress on the surviving component of the system. The Maximum Likelihood Estimators of parameters and their asymptotic distribution are obtained. Further the Maximum Likelihood Estimator and Bayes Estimator of reliability function are obtained using the data from a life-testing experiment. Computation of estimators is illustrated through simulation study.

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